Changing camera location for one frame changes it for everything
You need to add keyframes to set the location at different points in the animation - otherwise Blender is not aware of how you want the object to move and assumes you are just moving it to its new 'static' location.
You should set a keyframe at the start of the motion - this can be achieved by simply hitting I and selecting 'Location' (or whatever property you are keyframing) while in the 3D Viewport. Then move to the end frame and move the camera and, again, add a keyframe using the same process. Your camera should now move between those keyframes when you play the animation or move through the timeline.